If I was behind a router that does not respond to ICMP or listen/NAT any services on UDP/TCP. Am I susceptible to a DDoS attack?
Yes. At least on the bandwidth side, there could be more data coming in than the Internet downlink can handle. A severely congested interface loses massive amounts of packets and becomes unusable.
A faster Internet access makes a bandwidth-based attack harder, but any bandwidth can be exceeded with DDoS, especially when using amplification techniques.
With destination NAT on the router, you're additionally susceptible to have the NATed service or device overloaded. Depending on the firewall and the host configuration, a targeted (D)DOS attack may be much easier to achieve than a purely bandwidth-based attack.